Simple Machines Worksheet A
1. The Ramseys are moving to a new town, so they have called in the ACME moving company to take care
of their furniture. Debbie, one of the movers, slides the Ramseys’ 2200-N china cabinet up a 6.0-m-long
ramp to the moving van, which stands 1.0-m off the ground.
2200N
a) What is the ideal mechanical advantage of the incline?
ௗ೔೙
݀௜௡ = 6݉
‫= ܣܯܫ‬
ௗ೚ೠ೟
1m
݀௢௨௧ = 1݉
଺௠
‫ܨ‬௜௡ =?
‫= ܣܯܫ‬
ଵ௠
‫ܨ‬௢௨௧ = 2200ܰ
‫ = ܣܯܫ‬6
b) If Debbie must exert a 500-N force to move the china cabinet up the ramp with a constant speed,
what is the actual mechanical advantage of the ramp?
ி
‫ܨ‬௜௡ = 500ܰ
‫ = ܣܯ‬ி೚ೠ೟
೔೙
2200
‫= ܣܯ‬
500
‫ = ܣܯ‬4.4
c) What is the efficiency of the ramp?
ெ஺
ସ.ସ
%݂݂݁ = ூெ஺ × 100 = ଺ × 100
%݂݂݁ = 73%
d) What is the force of friction on the ramp? (The force of friction is the difference in the force
needed without friction, from IMA, and the actual force used on the real machine with friction)
‫ = ܣܯܫ‬6 , this is how much
What force would I use
Therefore, subtract ideal force
you multiply your input force
without friction
from actual force used to get friction
ி
‫ = ܣܯܫ‬೚ೠ೟
500ܰ − 366.7ܰ = 133.3ܰ = ‫ܨ‬௙
without friction.
In ideal Machine 6 =
ଶଶ଴଴ே
6=
‫ܨ‬௙ = 133.3ܰ
ி೔೙
ଶଶ଴଴ே
‫ܨ‬௜௡ = 366.7ܰ
(without friction)
2. Jack and Jill went up the hill to fetch a pail of water. At the well, Jill used a force of 20.0N to turn a
crank handle of radius 0.400m that rotated an axle of radius 0.100m, so she could raise a 60.0N bucket
of water.
a) What is the ideal mechanical advantage of the wheel? (Radii are proportional to distance)
0.4m
ௗ
‫ܨ‬௜௡
݀௜௡ = 0.4݉
‫ = ܣܯܫ‬ௗ ೔೙
0.1m
ி೔೙
‫= ܣܯܫ‬
݀௢௨௧ = 0.1݉
‫ܨ‬௜௡ = 20ܰ
‫ܨ‬௢௨௧ = 60ܰ
ி೔೙
೚ೠ೟
଴.ସ௠
଴.ଵ௠
IMA = 4
b) What is the actual mechanical advantage of the wheel?
ி
‫ = ܣܯ‬ி೚ೠ೟
‫ = ܣܯ‬ଶ଴ே = 3
೔೙
଺଴ே
c) What is the efficiency of the wheel?
ெ஺
ଷ
%݂݂݁ = ூெ஺ × 100 = ସ × 100
%݂݂݁ = 75%
‫ܨ‬௢௨௧
4. A jackscrew with a handle 30.0 cm long is used to lift a car sitting on the jack. The car rises 2.0 cm for every
full turn of the handle. What is the ideal mechanical advantage of the jack?
௜௡ 0.3
௜௡ 2௜௡
೔೙
௢௨௧ 0.02
௜௡ 2
0.3
௜௡ ?
௜௡ 1.885
௢௨௧ 60
೚ೠ೟
.
IMA = 94
.
5. Tom’s favorite pastime is fishing.
a) How much work is required for Tom to reel in a 10.0-kg bluefish from the water’s surface to the deck
of a fishing boat, 5.20 m above the water, if the reel of his fishing pole is 85.0% efficient?
.
.
௜௡ ?
೚ೠ೟ 100
85% 100
೔೙
௢௨௧ 5.2
10
௜௡ ?
௢௨௧ 10 9.81
98.1
85%
ଶ
೚ೠ೟ ೚ೠ೟
೔೙
೚ೠ೟
100
6.00 10 b) If Tom supplies a force of 15 N to the reel’s crank handle, what is the actual mechanical advantage of
the fishing pole?
.
೚ೠ೟ 6.5
೔೙
c) What is the ideal mechanical advantage of the fishing pole?
100
.
85% 100
7.7
6. Clyde, a stubborn 3500-N mule, refuses to walk into the barn, so Farmer MacDonald must drag him up a
5.0-m ramp to his stall, which stands 0.50-m above ground level.
a) What is the ideal mechanical advantage of the ramp?
௜௡ 5
೔೙
೚ೠ೟
0.5m
௢௨௧ 0.5
.
௜௡ ?
௢௨௧ 3500
10
3500N
b) If Farmer MacDonald needs to exert a 450-N force on the mule to drag him up the ramp with a constant
speed, what is the actual mechanical advantage of the ramp?
௜௡ 450
೚ೠ೟
೔೙
7.8
c) What is the efficiency of the ramp?
100
.
100
78%
SM 1. The efficiency of a squeaky pulley system is 73 %. The pulleys are used to raise a mass. What force is
exerted on the machine if a rope is pulled 18.0 m in order to raise a 58 kg mass a height of 3.0 m?
݂݂݁ = 73%
݂݂݁ =
‫ܨ‬௜௡ =?
݂݂݁ =
݀௜௡ = 18.0݉
ௐ೚ೠ೟
× 100
ி೚ೠ೟ ௗ೚ೠ೟
73% =
݉ = 58݇݃
ௐ೔೙
ி೔೙ ௗ೔೙
× 100
(ହ଺ଽே)(ଷ௠)
(ி೔೙ )(ଵ଼௠)
× 100
݀௢௨௧ = 3.0݉
‫ܨ‬௜௡ = 129.9ܰ
‫ܨ‬௜௡ = 1.3 × 10ଶ ܰ
݉
‫ܨ‬௢௨௧ = ݉݃ = ሺ58݇݃ሻ ቀ9.91 ଶ ቁ = 569ܰ
‫ݏ‬
SM 2. The ramp in this figure is 18 m long and 4.5 m high.
a. What force parallel to the ramp (FA) is required to slide a 25 kg box at constant speed to the top of the ramp
if friction is disregarded?
‫ܨ‬௚∥ = ‫ܨ‬௚ ‫ߠ݊݅ݏ݃݉ = ߠ݊݅ݏ‬
݉ = 25݇݃
‫ܨ‬௚∥ = (25݇݃)(9.81 ௦మ )sin(14.5௢ )
Must push against
݃ = 9.81 ௦మ
‫ܨ‬௚∥ = 61.4ܰ
௠
4.5
ߠ = ‫ି݊݅ݏ‬ଵ ൬ ൰ = 14.5௢
18
b. What is the IMA of the ramp?
݀௜௡ = 18݉
௠
‫ = ܣܯܫ‬ௗ ೔೙
ௗ
‫ = ܣܯܫ‬ସ.ହ௠
೚ೠ೟
ଵ଼௠
݀௢௨௧ = 4.5݉
‫ = ܣܯܫ‬4
c. What are the real MA and the efficiency of the ramp if a parallel force (FA) of 75 N is actually required?
ி
ଶସହ.ଶହே
‫ = ܣܯ‬ி೚ೠ೟ = ଻ହே = 3.27 = ‫ܣܯ‬
‫ܨ‬௢௨௧ = ݉݃ = ሺ25݇݃ሻ ቀ9.81 ௦మ ቁ = 245.25ܰ
௠
೔೙
‫ܣܯ‬
3.27
× 100 =
× 100 = 81.8%
‫ܣܯܫ‬
4
SM 3. A person must move a large stone in her backyard. She gets a plank that is 3.50 m long to use as a lever
and she wedges one end of the plank under the large stone. A smaller stone, 0.750 m from the large one, serves
݂݂݁ =
as a pivot. The plank makes an angle of 20.0 o with the ground. When she pushes down on the end of the plank
with a force of 210 N, the large stone begins to move.
‫ܨ‬௜௡ = 210ܰ
݀௜௡ = 2.75݉
݀௢௨௧ = 0.75݉
You can use the lever arms as distances
‫ܨ‬௢௨௧ =?
ܹ௜௡ ≥ ܹ௢௨௧
‫ܨ‬௜௡ ݀௜௡ ≥ ‫ܨ‬௢௨௧ ݀௢௨௧
ሺ210ܰሻሺ2.75݉ሻ = ሺ‫ܨ‬௢௨௧ ሻ(0.75݉)
a. What upward force is being exerted against the large stone?
‫ܨ‬௢௨௧ = 770ܰ
b. What is the mechanical advantage of the lever?
‫= ܣܯ‬
ி೚ೠ೟
ி೔೙
‫ܨ‬௢௨௧ = 7.70 × 10ଶ ܰ
଻଻଴ே
= ଶଵ଴ே = 3.67
SM 4. Why is it easier to loosen the lid from the top of a paint can with a long handled screwdriver than with a
short-handled screwdriver?
More Leverage: Longer handle means more input distance so there is more output force
SM 5. You are attempting to move a large rock using a long lever. Is it more effective to place the lever’s axis
of rotation nearer to your hands or nearer to the rock? Explain.
It is more effective to put the lever’s axis (fulcrum) nearer the rock so that your input distance is greater
than output distance thereby making the output force bigger than the input force.
SM 6. A pulley system lifts a 1345 N weight a distance of 0.975 m. Paul pulls the rope a distance of 3.90 m,
exerting a force of 375 N.
a. What is the IMA of the system?
‫ܨ‬௢௨௧ = 1345ܰ
‫ = ܣܯܫ‬ௗ ೔೙ = ଴.ଽ଻ହ௠
b. What is the MA?
‫= ܣܯ‬
݀௢௨௧ = 0.975݉
݀௜௡ = 3.90݉
‫ܨ‬௜௡ = 375ܰ
c. How efficient is the system?
ௗ
ଷ.ଽ௠
೚ೠ೟
‫ = ܣܯܫ‬4
ி೚ೠ೟
ி೔೙
=
ଵଷସହே
ଷ଻ହே
= 3.587
݂݂݁ = ூெ஺ × 100 =
ெ஺
ଷ.ହ଼଻
ସ
‫ = ܣܯ‬3.59
× 100 = 89.7%
SM 7. If you were to use a machine to increase the output force, what factor would have to be sacrificed? Give
an example where this occurs.
You have to sacrifice the distance the output force moves compared to the distance the input moves.
SM 8. A leveling foot on an air track is a screw. It can be turned to move it into or out of the base of the air
track to make the end go up or down. Suppose the leveling screw on a particular air track has 15 threads per
cm. The screw has a knob of diameter 1.5 cm to make it easier to turn.
1ܿ݉ ‫ = ݌ݑ‬15 ‫ݐ ݂݋ ݏ݊݋݅ݐݑ݈݋ݒ݁ݎ‬ℎ݁ ‫ݐ‬ℎ‫݀ܽ݁ݎ‬
a. In one complete rotation of the screw, how far is the air track lifted?
Therefore
ଵ ௥௘௩௢௟௨௧௜௢௡
= ݀௢௨௧
ଵ
ቀ
ଵ ௖௠ ௨௣
ଵହ ௥௘௩௢௟௨௧௜௢௡௦
ቁ = 0.0667ܿ݉ ‫݌ݑ‬
b. What is the IMA of the screw?
݀௜௡ = ܿ݅‫ = ߨ݀ = ݁ܿ݊݁ݎ݂݁݉ݑܿݎ‬ሺ1.5ܿ݉ሻߨ = 4.71ܿ݉
‫= ܣܯܫ‬
ௗ೔೙
=
ସ.଻ଵ௖௠
= 70.69
‫ = ܣܯܫ‬70.7
c. If a force of 0.50 N is necessary to rotate the knob to lift the air track, what is the weight of the end of the air
track lifted, assuming the screw is 80% efficient?
Weight = output force
Need to know MA
݂݂݁ = 80%
‫ܨ‬௜௡ = 0.50ܰ
ௗ೚ೠ೟
଴.଴଺଺଻௖௠
݂݂݁ = ூெ஺ × 100
ெ஺
ெ஺
80% = ଻଴.଻ × 100
‫ = ܣܯ‬56.5
‫= ܣܯ‬
ி೚ೠ೟
56.5 = ଴.ହே
‫ܨ‬௢௨௧ = 28.3ܰ
ி೚ೠ೟
ி೔೙